From my brief experience running Skype on multiple devices; if you can get both of them online at the same time for a while, it'll sync up eventually. If it's always one or the other, good luck (there's a reason I stopped running it on two devices)
I have my phone running right next to my laptop. It still doesn't handle things right (Signal does). If one is offline for a bit then sometimes it syncs, sometimes it leaves unread indicators.
